1. Filed of the Invention
The present invention relates to the petroleum industry, and more particularly to petroleum reservoir characterization by construction of a representation of the reservoir referred to as reservoir model. In particular, the invention relates to a method of constructing a facies map associated with the reservoir model. This map is used to update a reservoir model after acquiring new measurements within the petroleum reservoir.
2. Description of the Prior Art
Optimization and development of petroleum reservoirs is based on the most accurate possible description of the structure, the petrophysical properties, the fluid properties, etc., of the studied reservoir. A tool is used accounting for these aspects in an approximate way which is a reservoir model. Such a model is a model of the subsoil, representative of both its structure and its behavior. Generally, this type of model is represented in a computer and it is referred to as a numerical model.
These models which are well known and widely used in the petroleum industry, allow determination of many technical parameters relative to prospecting, study or development of a reservoir such as, for example, a hydrocarbon reservoir. In fact, a reservoir model is representative of the structure of the reservoir and of the behavior thereof. It is thus for example possible to determine which zones are the most likely to contain hydrocarbons, the zones in which it can be interesting or necessary to drill an injection well in order to enhance hydrocarbon recovery, the type of tools to use, the properties of the fluids used and recovered, etc. These interpretations of reservoir models in terms of “technical development parameters” are well known, even though new methods are regularly developed. It is thus crucial, in the petroleum industry, to construct a model as precise as possible. Integration of all the available data is therefore essential.
The purpose of a reservoir model thus is to best account for all the information relative to a reservoir. A reservoir model is representative when a reservoir simulation provides historical data estimations that are very close to the observed data. What is referred to as historical data are the production data obtained from measurements in wells in response to the reservoir production (oil production, water production of one or more wells, gas/oil ratio (GOR), production water proportion (water cut)), and/or repetitive seismic data (4D seismic impedances in one or more regions, etc.). A reservoir simulation is a technique allowing simulation of fluid flows within a reservoir by software referred to as flow simulator.
History matching modifies the parameters of a reservoir model, such as permeabilities, porosities or well skins (representing damages around the well), fault connections, facies, etc., in order to minimize the differences between the simulated and measured historical data. The parameters can be linked with geographic regions, such as permeabilities or porosities around one or more wells, or within one or more facies.
A reservoir model has a grid with N dimensions (N>0 and generally two or three). Each cell is assigned the value of a property characteristic of the zone which is being studied. It can be, for example, the porosity or the permeability distributed in a reservoir. FIG. 1 shows a facies map of a petroleum reservoir, making up a two-dimensional reservoir model. The grid pattern represents the cells. The grey cells represent a reservoir facies zone and the white cells represent a non-reservoir facies zone.
The value of a property characteristic of the zone is referred to as regionalized variable. It is a continuous variable, spatially distributed, and representative of a physical phenomenon. From a mathematical point of view, it is simply a function z(u) taking a value at each point u (the cell of the grid) of a field of study D (the grid representative of the reservoir). However, the variation of the regionalized variable in this space is too irregular to be formalized by a mathematical equation. In fact, the regionalized variable represented by z(u) has both a global aspect relative to the spatial structure of the phenomenon studied and a random local aspect.
This random local aspect can be modelled by a random variable (VA). A random variable is a variable that can take a certain number of realizations z according to a certain probability law. Continuous variables such as seismic attributes (acoustic impedance) or petrophysical properties (saturation, porosity, permeability) can be modelled by VAs. Therefore, at point u, the regionalized variable z(u) can be considered to be the realization of a random variable Z.
However, to properly represent the spatial variability of the regionalized variable, it must be possible to take into account the double aspect, both random and structured. One possible approach, of probabilistic type, involves the notion of random function. A random function (FA) is a set of random variables (VA) defined in a field of study D (the grid representative of the reservoir), i.e. {Z(u), u*D}, also denoted by Z(u). Thus, any group of sampled values {z(u1), . . . , z(un)} can be considered to be a particular realization of random function Z(u)={Z(u1), . . . , Z(un)}. Random function Z(u) allows accounting for both the locally random aspect (at u*, the regionalized variable z(u*) being a random variable) and the structured aspect (via the spatial probability law associated with random function Z(u)).
The realizations of a random function provide stochastic reservoir models. From such models, it is possible to appreciate the way the underground zone studied works. For example, simulation of the flows in a porous medium represented by numerical stochastic models allows, among other things, to predict the reservoir production and thus to optimize its development by testing various scenarios.
Construction of a stochastic reservoir model can be described as follows:    First, static data are measured in the field (logging, measurements on samples taken in wells, seismic surveys, . . . ) and, dynamic data are measured (production data, well tests, breakthrough time, . . . ), whose distinctive feature is that they vary in the course of time as a function of fluid flows in the reservoir.    Then, from the static data, a random function characterized by its covariance function (or similarly by its variogram), its variance and its mean is defined.    A set of random numbers drawn independently of one another is defined: it can be, for example, a Gaussian white noise or uniform numbers. Thus, an independent random number per cell and per realization is obtained,    Finally, from a selected geostatistical simulator and from the set of random numbers, a random draw in the random function is performed, giving access to a (continuous or discrete) realization representing a possible image of the reservoir. Conventionally, the random draw is performed in a hierarchical context. First, the reservoir is randomly populated by a realization of the random function associated with the facies, conditionally to the punctually observed facies. Then, the porosity is generated randomly on each facies, conditionally to the porosity data obtained on the facies which is considered. The horizontal permeability is then simulated according to its associated random function, conditionally to the facies and to the porosities drawn before, and to the permeability measurements taken in the field. The reservoir is then populated by a random realization of the vertical permeability, conditionally to all the previous simulations and to the permeability punctually obtained data.
At this stage, the dynamic data have not been considered. They are integrated in the reservoir models via an optimization or a calibration. An objective function measuring the difference between the dynamic data measured in the field and the corresponding responses simulated for the model under consideration is defined. The goal of the optimization procedure is to modify little by little this model so as to reduce the objective function. Parametrization techniques allow these modifications to be provided while preserving coherence with respect to the static data.
In the end, the modified models are coherent with respect to the static data and the dynamic data. It must be possible to update these models complete. When new data are available, the model has to be modified to also take account of these new data. Moreover, the calibration and parametrization techniques are improving continuously. Consequently, reservoir engineers frequently need to go back over reservoir models elaborated and calibrated in the past. The goal is to refine these models and to update them by means of the data acquired since the time when the model had been initially elaborated.
However, an essential difficulty still remains when going back over numerical models elaborated in the past. In fact, to apply a method allowing refinement of the calibration of an existing realization, the number of random numbers which, when given to the geostatistical simulator, provides the numerical model (the realization) in question has to be known. Now, in general, this information no longer exists. Similarly, the variogram (or covariance) model characterizing the spatial variability in the underground zone of the attribute represented and necessary to characterize the random function is no longer known. The latter point is less important insofar as a study of the existing numerical model can allow finding this variogram again.
French Patent 2,869,421 discloses a method allowing reconstruction of numerical stochastic models for a previously determined random function, to identify a set of random numbers which, given as input data to a geostatistical simulator, leads to a realization similar to the numerical model being considered. However, this technique applies to continuous variables representative, for example, of the porosity to the case of a reservoir comprising a single facies.